20 Oct
2011
20 Oct
'11
5:17 p.m.
On 20 Oct 2011 at 15:45, Fred Cisin wrote:
I have to disagree. Significant digits are not the
same as having
CORRECT info or data. And 24 binary significat digits is absolutely NOT
the same as 24 CORRECT binary digits.
As I said, bonehead numerical methods. Not to be confused with the
mathematics of errors, although the two are somewhat related.
If you have 4 decimal digits of significance in your "floating point"
(actually, exponential) notation (floating point in BDP means
something a bit different) mantiassa and subtract 0.9998E4 from
0.9999E4, you get an answer of 0.1000E1, but only one digit has *any*
singificance--the remainder is garbage. Chain a few calculations of
this sort and you'll soon lose *all* significance and the machine
will manufacture meaningless "answers" for you.
Use some of this sort of math involving trig functions near their
limits and you can discover that between two systems claiming the
same precision that answers can be wildly different--the result of
computing using differently-flavored garbage.
My beef with some compiler writers is that they'll often do you a
favor by silently rearranging expressions to make use of distributive
or associative properties and that series that *used* converge neatly
now no longer does.
--Chuck